Two-level Default Theories

摘要

Default Logic employs assumption-based default rules to draw plausible consequences in face of incomplete information. In ontology representation, there are two kinds of relations between concepts: subsumption relation and default subsumption relation. Subsumption relation is transitive, whereas default subsumption relation is transitive by default. Both default transitivity of default subsumption and default inheritance of default property should be represented as defaults about defaults, i.e. two-level defaults. None of existing default logics can represent two-level defaults. In this paper, we propose two-level default theories which augment default theories with two-level defaults. A two-level default theory can be divided into two levels and its extensions can be generated by two steps. We prove that normal two-level default theories cannot reduce to normal default theories. Specifically, there is a normal two-level default theory such that there exists no normal default theory such that they share the same set of extensions.